3 Qualitative mathematical modelling (stage 2)

In this work we have been guided by a strategy of model building that recognises a practical trade-off between realism, generality and precision when building and analysing models of complex systems (Levins, 1966, 1998). To obtain a manageable and useful model, one typically sacrifices one attribute for the other two. Qualitative mathematical models emphasise generality and realism, but lack precision, while numerical simulation models can be both precise and realistic but are not generalisable (i.e. application of the model to changed circumstance requires reparameterisation). A third approach is statistical, and emphasises precision and generality. Here there are precise insights into the general pattern of correlations among variables, but at the cost of causal understanding of the processes involved. In practice we seek a robust strategy that considers combinations of different modelling approaches, such that models are mutually informative and build upon the strengths and insights of other approaches. The impact and risk analysis for BAs is being informed by all three modelling approaches. In this section we describe the basic methods underpinning qualitative mathematical modelling.

Qualitative mathematical modelling serves three roles within BA’s receptor impact modelling strategy. Firstly, sign-directed graphs (e.g. see Figure 5), built for each potentially impacted landscape class, document current understanding of how the landscape class ecosystem ‘works’ including key interactions between the system’s physical, chemical and biological components, and their dependence on hydrology.

Secondly, through qualitative predictions of increase, decrease or no change, the models capture the direct and indirect effects that are anticipated to occur following a sustained change to the surface water or groundwater regimes that maintain the ecosystem of the landscape class. Lastly, BAs use the hydrological factors identified in the models, and the direct and indirect effects that they predict, to identify appropriate hydrological response variables and receptor impact variables for the next stages of the receptor impact model strategy.

The BA methodology (Barrett et al., 2013) requires an explicit assessment of the potential direct, indirect and cumulative impacts of CSG and coal mining development on water resources, together with an analysis of the associated uncertainties. A coherent analysis of uncertainty necessitates a probabilistic analysis, so in effect the BA methodology requires a probabilistic landscape-level assessment of the risks that coal resource development poses to water resources. The BA methodology goes on to define direct impacts as those associated with CSG and coal mining developments that impact on natural resources without intervening agents or pathways, whilst indirect impacts are defined as those impacts on receptors (within water-dependent assets) that are produced as a result of a (simple or complex) pathway of cause and effect.

It is important to recognise that the BA methodology sets an ambitious target, seeking to predict how direct, indirect and cumulative impacts on hydrology by development affect receptors at multiple time points, but does not describe how to meet it. The receptor impact modelling strategy is designed to operationalise the aspirations of the BA methodology, and this process begins by distinguishing direct and indirect impacts in a conceptual model of the potential stress imposed on the ecosystem by coal resource development.

Qualitative mathematical modelling depicts the stressor conceptual model as a sign-directed graph wherein the direct effects between model variables are depicted as arcs ending in an arrowhead for positive direct effects, and arcs ending in a filled circle for negative direct effects (Section 3.1.1). The potential direct effect of coal resource development is identified by at least one negatively or positively signed arc between a hydrological response variable and one or more of the model’s other variables.

Within the sign-directed graph, a pathway with one arc is formally defined as a ‘direct effect’, whereas a pathway consisting of two or more arcs, which must therefore involve other intermediate variables, is formally defined as an ‘indirect effect’ (Section 3.1.1). The direct impacts of coal resource development are thereby depicted within the sign-directed graph as arcs of length one between a hydrological response variable and another model variable. Indirect impacts are identified as arcs of length two or more between a hydrological response variable and another model variable. Finally, cumulative impacts are depicted by changes to two or more potentially interacting hydrological response variables, with concomitant direct and indirect impacts arising from this.

When considering potential changes (perturbations) to the hydrological response variables that maintain landscape class ecosystems, it is important to distinguish between ‘press’ and ‘pulse’ perturbations. A press perturbation is defined as a sustained, or long-term, change in the value of a biological or physiochemical parameter that is associated with one or more variables that causes a shift in the equilibrium values of the system’s variables. This is in contrast to a pulse perturbation, which is a sudden increase or decrease in a variable that only moves the system away from its equilibrium temporarily, but does not necessarily result in a permanent shift to a new equilibrium state. Press-type perturbations are typically defined in terms of experimental manipulations of ecosystems (Dambacher et al., 2002; Schmitz, 1998). In a BA qualitative model, press perturbations are caused by CSG or coal mine induced changes to hydrological response variables. It is acknowledged that pulse perturbations and other categories of disturbance, such as ramp disturbance (Lake, 2000), are also of interest to BA. Press perturbations and other perturbation types may be assessed by the quantitative receptor impact model methodology described in the following chapters.

The distinction between press and pulse perturbations is important because the direct and indirect effects of pulse perturbations are typically minimal or short-lived. These perturbations typically occur over time frames that are much smaller than the generation time of the biological variables of interest. Unless the magnitude of the perturbation is so large that the system is moved to a new equilibrium state, there will be no permanent shift in the equilibrium level of the system variables, but only transient variations in their levels of abundance.

The Bioregional Assessment Programme, however, is principally concerned with press perturbations – that is, changes in hydrological response variables that are sustained for a relatively long time period, say many decades – and hence over much larger time frames than the generation times of the potentially impacted biological variables. The sustained nature of this type of perturbation provides time for the knock-on effects to be felt throughout the entire system. Although the quantitative receptor impact modelling strategy may account for both press and pulse perturbations (see following chapters), the implementation of the qualitative mathematical modelling focuses on press perturbations, and deliberately describes potential impacts on hydrological response variables in terms of changes in their long-term (e.g. 30 years) averages. Some pulse perturbations (e.g. the failure of a tailings dam) are assumed to be adequately managed by site-based risk management and mitigation procedures and are not assessed further in BAs.

This approach to defining and identifying direct, indirect and cumulative impacts is consistent with, and operationalises, the definitions in the BA methodology, and importantly provides a transparent platform for a coherent probabilistic analysis of direct effects (cumulative or otherwise) together with a qualitative mathematical analysis of indirect effects where relevant (see below).